CHAPTER 3 HW SOLUTIONS
3.2
(a)
(b)
Mean = 7
Median = 7
Mode = 7
Range = 9
Variance = 10.8
Interquartile range = 5
Standard deviation = 3.286
Coefficient of variation = (3.286/7)•100% = 46.94%
Z scores: 0, -0.913, 0.609, 0, -1.217, 1.522
None of the Z scores is larger than 3.0 or smaller than -3.0. There is no outlier.
Since the mean equals the median, the distribution is symmetrical.
(c)
(d)
3.6
(a)
(b)
Grade X
Grade Y
Mean
575
575.4
Median
575
575
Standard deviation
6.4
2.1
If quality is measured by the average inner diameter, Grade X tires provide slightly better
quality because X’s mean and median are both equal to the expected value, 575 mm. If,
however, quality is measured by consistency, Grade Y provides better quality because,
even though Y’s mean is only slightly larger than the mean for Grade X, Y’s standard
deviation is much smaller. The range in values for Grade Y is 5 mm compared to the
range in values for Grade X which is 16 mm.
(c)
Mean
Grade X
575
Grade Y, Altered
577.4
Median
575
575
Standard deviation
6.4
6.1
In the event the fifth Y tire measures 588 mm rather than 578 mm, Y’s average inner
diameter becomes 577.4 mm, which is larger than X’s average inner diameter, and Y’s
standard deviation swells from 2.07 mm to 6.11 mm. In this case, X’s tires are providing
better quality in terms of the average inner diameter with only slightly more variation
among the tires than Y’s.
3.10 Excel output:
Product
Calories
Dunkin’ Donuts Iced Mocha Swirl latte
(whole milk)
Starbucks Coffee Frappuccino blended
coffee
Dunkin’ Donuts Coffee Coolatta (cream)
Starbucks Iced Coffee Mocha Expresso
(whole milk and whipped cream)
Starbucks Mocha Frappuccino blended
coffee (whipped cream)
Starbucks Chocolate Brownie Frappuccino
blended coffee (whipped cream)
Starbucks Chocolate Frappuccino Blended
Crème (whipped cream)
(a)
Calories: mean = 380
median = 350
Fat
240
Calories Fat Z
Z Score
Score
8
-1.24
-1.07
260
3.5
-1.06
-1.69
350
350
22
20
-0.27
-0.27
0.86
0.58
420
16
0.35
0.03
510
22
1.15
0.86
530
19
1.33
0.44
1st quartile = 260
3rd quartile = 510
(b)
(c)
(d)
3.56
Fat: mean = 15.8
median = 19
1st quartile = 8
3rd quartile = 22
Calories: variance = 12800 standard deviation = 113.1
range = 290
interquartile range = 250 CV = 29.77%
None of the Z scores are less than -3 or greater than 3. There is no outlier in calories.
Fat: variance = 52.82 standard deviation = 7.3
range = 18.5
Interquartile range = 14
CV = 46.04%
None of the Z scores are less than -3 or greater than 3. There is no outlier in fat.
Calories are slightly right-skewed while fat is slightly left-skewed.
The mean calories is 380 while the middle ranked calorie is 350. The average scatter of
calories around the mean is 113.14. 50% of the calories are scattered over 250 while the
difference between the highest and the lowest calories is 290.
The mean fat is 15.79 grams while the middle ranked fat is 19 grams. The average
scatter of fat around the mean is 7.27 grams. 50% of the fat is scattered over 14 grams
while the difference between the highest and the lowest fat is 18.5 grams.
mean = 43.89
median = 45
1st quartile = 18 3rd quartile = 63
range = 76
interquartile range = 45
variance = 639.2564
standard deviation = 25.28
coefficient of variation = 57.61%
(a)
(b)
(c)
Box-and-whisker Plot
Time
10
50
70
90
The distribution is skewed to the right because there are a few policies that require
an exceptionally long period to be approved even though the mean is smaller than the
median.
The mean approval process takes 43.89 days with 50% of the policies being
approved in less than 45 days. 50% of the applications are approved between 18 and
63 days. About 67% of the applications are approved between 18.6 to 69.2 days.
(d)
3.60
30
(a), (b)
Mean
Median
Standard Deviation
Sample Variance
Range
First Quartile
Third Quartile
Time
Office I Office II
2.214
2.012
1.54
1.505
1.7180
1.8917
2.9517
3.5786
5.8
7.47
0.93
0.6
3.93
3.75
Interquartile Range
Coefficient of Variation
3
77.60%
3.15
94.04%
(c)
Box-and-whisker Plot
Time (Office II)
Time (Office I)
0
(d)
3.62
2
4
6
8
Times to clear problems at both central offices are right-skewed.
Times to clear problems for Office I are less dispersed about the mean than times to
clear problems for Office II, even though the mean for Office I times is higher
(2.214) than that for Office II (2.012).
(a), (b)
Excel output:
In-State Tuition/Fees
Mean
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
First Quartile
Third Quartile
Interquartile Range
Coefficient of
Variation
6841.815534
6340
7062
2212.221516
4893924.034
4.295740452
1.350377978
14466
3094
17560
704707
103
5378
8143
2765
32.33%
Out-of State Tuition/Fees
17167.71
16340
14901
4274.009
18267150
-0.33509
0.524429
20007
8965
28972
1768274
103
13928
20134
6206
24.90%
3.62
cont.
(c)
Box-and-whisker Plot
Out-of State
Tuition/Fees
In-State
Tuition/Fees
3000
8000
13000
18000
23000
28000
Both in-state and out-of-state tuition and fees are right skewed.
cov X , Y 
 0.4911
S X SY
(d)
r
(e)
Both in-state and out-of-state tuition and fees are right skewed due to the outliers in
the right tails. There is a moderate positive linear relationship between in-state and
out-of-state tuition and fees. Those schools with a high in-state tuition and fees tend
to also have a high out-of-state tuition and fees.
3.68
(a), (b) Excel output:
Average Fan Cost Regular
Local TV, Other
Player
National Income
Ticket$ Index
season gate radio and Local
compensation and other from
receipts
cable
Operating and benefits local
Baseball
($millions) ($millions) Revenue
Expenses Operations
Minimum
6.61
84.89
6.4
0.5
2.8
30.5
35
-52.9
First
15.2 124.25
30.2
10.9
13.9
49.4
46.9
-18.5
Quartile
Median
17.83 143.475
47.55
16.35
29.05
70.8
50.5
-8.35
Third
20.84 160.76
62.1
23.6
37
92.8
58.5
1.9
Quartile
Maximum
39.68 228.73
98
56.8
61.5
118.5
84.2
40.9
Mean
18.1333 144.5737
46.1367
19.0467 27.5933
71.3567
54.6467
-8.3733
Variance
35.9797 843.4552 512.5445 151.0184 234.6186
663.8405 176.4081 428.1531
Standard
5.9983 29.0423
22.6394
12.2890 15.3173
25.7651
13.2819
20.6919
Dev
Range
33.07 143.84
91.60
56.30
58.70
88.00
49.20
93.80
Interquartile
5.64
36.51
31.90
12.70
23.10
43.40
11.60
20.40
Range
Coefficient 33.08% 20.09%
49.07%
64.52% 55.51%
36.11%
24.30% -247.12%
of Variation
(c)
Box-and-whisker Plot
Income from Baseball
Operations
National and other local
Expenses
Player compensation
and benefits
Other Local Operating
Revenue
Local TV, radio and
cable ($millions)
Regular season gate
receipts ($millions)
Fan Cost Index
Average Ticket$
-60
(d)
-10
40
90
140
190
Average ticket prices, local TV, radio and cable receipts, national and other local
expenses are skewed to the right; fan cost index is slightly skewed to the right; all
other variables are pretty symmetrical.
r = 0.3985. There is a moderate positive linear relationship between the number of wins
and player compensation and benefits.
240
3.72
Excel output:
Mean
Median
Mode
Standard Deviation
Sample Variance
Range
Minimum
(a)
(b)
7.5273
7.263
7.649
1.631227
2.660901
7.416
5.469
Maximum
Sum
Count
First Quartile
Third Quartile
Interquartile Range
Coefficient of Variation
12.885
376.365
50
6.353
8.248
1.895
21.67%
mean = 7.5273, median = 7.263, first quartile = 6.353, third quartile = 8.248
range = 7.416, interquartile range = 1.895, variance = 2.6609, standard deviation =
1.6312, coefficient of variation = 21.67%
(c)
Box-and-whisker Plot
Spending
0
2
(d)
4
6
8
10
12
14
The data are skewed to the right.
The per capita spending by the 50 states are right skewed because a few states spend
a lot more than the rest.